How To Find Common Multiples Of Fractions

LCM of 2 numbers is the smallest mutual multiple or a positive integer which is divisible completely by both the numbers. LCM is the to the lowest degree common multiple betwixt two or more than numbers which is wholly divisible past them. Suppose the LCM of a and b is equal to c, then c should be evenly divisible past both a and b. To find LCM of more than ii numbers read here .

Nosotros will also larn to find the LCM of fractions using the formula and with the help of examples.

Table of contents:

Definition
Methods to Find LCM of ii numbers
- Listing Multiples
- Prime Factorization
- Division Method
- GCD Method
Solved Issues
LCM of Fractions
FAQs

What is LCM of two Numbers?

The LCM of Least Common Multiple of 2 numbers is the smallest number, divisible by the 2 numbers, evenly. Information technology is also known equally the Least Common Divisor or LCD.

For example, consider 2 numbers every bit x and four. Now, the smallest number that can be divided by 10 and four evenly, will exist 20. We tin as well notice the LCM using prime number factorisation method.

How to Discover LCM of Two Numbers?

In that location are iv chief methods to calculate the to the lowest degree mutual multiple of 2 numbers. These methods are:

Listing Multiples or Brute Force Method
Prime Factorization Method
Division Method or Ladder Method
GCD or GCF Method

Listing Multiples or Beast Strength Method of Finding LCM

In this method, the multiples of each number are listed until the starting time common multiple is found. Consider the case of 4 and 10. For this method, the multiples of 4 and 10 are to be listed.

Multiples of 4: four, 8, 12, 16, 20, 24, 28

Multiples of x: 10, twenty, 30, forty

Here, the number 20 is the start mutual multiple of both 4 and 10. So, the LCM of 4, 10 is xx.

Prime number Factorization Method of Finding LCM

The prime factorization is one of the nearly common ways of finding LCM. To find the LCM of two numbers thirty and 45, the steps are as follows:

Step i: To first list the prime factors of each number.

30 = 2 × 3 × 5
45 = iii × three × five

Step 2: Next multiply each factor the maximum number of times information technology occurs in either number.

If the same factor occurs more than once in both numbers, so multiply the factor the maximum number of times it occurs.

The occurrence of Numbers in the above example:

2: one time
3: two times
5: one time
LCM = two × 3 × 3 × 5 = 90

After computing the LCM, always bank check to be certain your reply can be divided evenly by both numbers.

Sectionalization Method or Ladder Method of Finding LCM

In this method, the two numbers are simultaneously divided with prime numbers until the division is even. When at that place are no more primes that evenly divide into both numbers, multiply the divisors to get the LCM. For example, consider four and 10 as ii

Division Method or Ladder Method of Finding LCM

Hither, the LCM of 24, 15 volition exist 2×two×ii×3×5=23×3×5=120

GCD or GCF Method of Finding LCM

This method is used only when the greatest mutual cistron of ii numbers is given. The formula used to find the LCM using the GCF or GCD is:

L.C.M. = a×b/ gcd(a,b)

For case, for 15 and 24, the GCF will be iii. So, the LCM will exist (15 × 24) / three = three.

Solved Examples

Example 1: Observe the 50.C.M of eighteen and 24 by using the division method?

Solution:

ii	18	24
2	9	12
ii	9	6
3	9	3
three	3	1
	ane	1

For numbers 18 and 24 = ii × ii × two × iii × 3 = 72 is the LCM.

Case 2: Find the Least Mutual Multiples of these sets of numbers: 3, 9, 21.

Solution:

Step one: List the prime factors of each.
3: 3
9: 3 × 3
21: 3 × 7

Pace two: Multiply each factor the maximum number of times it occurs in whatsoever of the numbers.

The occurrence of Numbers in the to a higher place example:

three: two times

7: 1 time

3 10 3 x 7 = 63

9 has 2 3s, and 21 has one seven, so we multiply three ii times, and vii once.

This gives us 63, the everyman number that can be divided evenly by three, ix, and 21.

Example 3: Notice the Least mutual gene of 12, 80.

Solution:

Step 1: List the prime factors of each.
12: 2 × 2 × three
fourscore: 2 × 2 × 2 × 2 × 5

Pace 2:
Multiply each gene the maximum number of times information technology occurs in either number.

Pace iii:

The occurrence of Numbers in the to a higher place case:

2: iv times

3: 1 time

five: 1 time

two ten 2 x ii 10 two ten 3 ten 5 =240

12 has one three, and eighty has iv 2'southward and one 5, then we multiply 2 4 times, three once, and five once.

This gives us 240, the lowest number that tin be divided by both 12 and eighty.

How to Notice LCM of Fractions?

LCM of two fractions will be the smallest common multiple which can be divided by the two fractions, wholly. Formula to find the LCM of ii fractions is:

50.C.M = \(\frac{LCM\, of\, the\, Numerators}{HCF\, of\, the\, Denominators}\)

Suppose a/b and c/d are 2 fractions. Then to find the LCM of a/b and c/d follow the below steps:

Step 1: Find LCM of the numerator i.eastward. LCM (a,c)

Step 2: Find HCF of denominator i.e. HCF (b,d)

Step 3: Put the values in the given formula

This is the shortcut method to detect the LCM of fractions.

Let us empathize with the help of an example .

Example: LCM of ⅘ and iii/7

As per the formula, LCM of any two fractions can exist found:

L.C.1000 = LCM of the numerators/HCF of denominators

At present first we need to notice the LCM of numerators.

Here the numerators are 4 and iii.

Therefore LCM (4,3) = 12

Second step is to find HCF of denominators.

Hence, HCF of 5 and 7 is:

v = 1 x 5

7 = one 10 7

HCF (5,7) = one

3rd pace will exist the last stride to put the values of LCM(4,3) and HCF(5,7) in the formula;

Therefore,

LCM (⅘ and 3/seven) = 12/1 = 12

Recheck: If 12 is the LCM of ⅘ and three/7, we should check if 12 is wholly divided past ⅘ and iii/7.

Hence,

12/(⅘) = (12 ten v)/four = 3 x 5 = xv

12/(three/vii) = (12 10 vii)/3 = 4 x 7 = 28

Hence, 12 is the right answer.

Oftentimes Asked Questions – FAQs

What is the formula to find LCM of two numbers?

LCM of whatsoever two numbers is the smallest common multiple or smallest common integer which is divisible by both the numbers completely. If LCM of a and b is c, then c should be divisible by a and b both.

What is the LCM of 2 and 4?

To find the LCM of 2 and four, let us write the multiples of both the numbers first.
Multiples of two = 2,4,half dozen,8,x,12…
Multiples of iv = 4,8,12,16,20,24..
Hence, the smallest mutual multiple here 4. Then, LCM (2,4) = 4
Is LCM of 2 numbers are the production of 2 numbers?
No, LCM of ii numbers is not their product but the smallest common multiple between them, which can be divided by both the numbers completely.

What is the LCM of 24 and 36?

To find LCM of 24 and 36 we tin can utilise prime factorisation method.
Prime factorisation of 24 = 2 x ii x ii x 3
Prime factorisation of 36 = 2 x ii ten 3 x three
Multiply each factor the maximum number of times it occurs in either number.
2 occurred 3 times and 3 occurred two times
Therefore, LCM (24,36) = two 10 2 x 2 x 3 x iii = 72

How to find LCM of two fractions?

To observe the LCM of ii fractions say a/b and c/d, we accept to use the formula:
LCM (a/b,c/d) = LCM of numerators/HCF of denominators = LCM(a,c)/LCM(b,d)

What is the LCM of iii and 7?

Multiples of 3 = 3, half dozen, 9, 12, 15, xviii, 21, 24,…
Multiples of seven = 7, 14, 21, 28, 35, ….
We can see the least mutual multiple here is 21. Therefore, LCM (3,vii) = 21